LMFDB - Embedded newform 169.10.a.c.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [169,10,Mod(1,169)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(169, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("169.1"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	169.a (trivial)

Newform invariants

comment:select newform

sage:traces = [9,-15] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$87.0410563117$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3 x^{8} - 3184 x^{7} + 4328 x^{6} + 3323368 x^{5} - 2832720 x^{4} - 1268725952 x^{3} + \cdots + 390142272000 $ x^9 - 3x^8 - 3184x^7 + 4328x^6 + 3323368x^5 - 2832720x^4 - 1268725952x^3 + 543328000x^2 + 114318839680x + 390142272000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 13^{2} $
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-7.18744$ of defining polynomial
Character	$\chi$	$=$	169.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-9.18744 q^{2} -148.535 q^{3} -427.591 q^{4} +1229.19 q^{5} +1364.65 q^{6} +8333.07 q^{7} +8632.44 q^{8} +2379.53 q^{9} -11293.1 q^{10} -75178.8 q^{11} +63512.0 q^{12} -76559.6 q^{14} -182577. q^{15} +139616. q^{16} -212677. q^{17} -21861.8 q^{18} -447815. q^{19} -525590. q^{20} -1.23775e6 q^{21} +690701. q^{22} +1.83926e6 q^{23} -1.28222e6 q^{24} -442219. q^{25} +2.57016e6 q^{27} -3.56314e6 q^{28} -1.21449e6 q^{29} +1.67742e6 q^{30} +3.80320e6 q^{31} -5.70253e6 q^{32} +1.11667e7 q^{33} +1.95396e6 q^{34} +1.02429e7 q^{35} -1.01746e6 q^{36} +1.69936e7 q^{37} +4.11427e6 q^{38} +1.06109e7 q^{40} +7.70454e6 q^{41} +1.13717e7 q^{42} +2.61552e7 q^{43} +3.21458e7 q^{44} +2.92489e6 q^{45} -1.68981e7 q^{46} -3.99265e7 q^{47} -2.07379e7 q^{48} +2.90864e7 q^{49} +4.06287e6 q^{50} +3.15899e7 q^{51} -2.84536e7 q^{53} -2.36132e7 q^{54} -9.24090e7 q^{55} +7.19347e7 q^{56} +6.65159e7 q^{57} +1.11581e7 q^{58} -6.33715e7 q^{59} +7.80683e7 q^{60} -1.20078e7 q^{61} -3.49417e7 q^{62} +1.98287e7 q^{63} -1.90920e7 q^{64} -1.02593e8 q^{66} -7.09554e7 q^{67} +9.09388e7 q^{68} -2.73193e8 q^{69} -9.41062e7 q^{70} +1.65210e8 q^{71} +2.05411e7 q^{72} +1.28511e8 q^{73} -1.56128e8 q^{74} +6.56849e7 q^{75} +1.91481e8 q^{76} -6.26470e8 q^{77} +6.32753e8 q^{79} +1.71615e8 q^{80} -4.28595e8 q^{81} -7.07850e7 q^{82} -1.34044e8 q^{83} +5.29250e8 q^{84} -2.61420e8 q^{85} -2.40299e8 q^{86} +1.80394e8 q^{87} -6.48977e8 q^{88} -8.05644e8 q^{89} -2.68722e7 q^{90} -7.86450e8 q^{92} -5.64906e8 q^{93} +3.66822e8 q^{94} -5.50449e8 q^{95} +8.47023e8 q^{96} +7.74868e7 q^{97} -2.67230e8 q^{98} -1.78890e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 15 q^{2} - 161 q^{3} + 1793 q^{4} - 1140 q^{5} - 2118 q^{6} + 1939 q^{7} - 7239 q^{8} + 33654 q^{9} - 46923 q^{10} + 5433 q^{11} + 4356 q^{12} - 4950 q^{14} + 347428 q^{15} - 400127 q^{16} - 248589 q^{17}+ \cdots + 1131074634 q^{99}+O(q^{100}) $ 9 * q - 15 * q^2 - 161 * q^3 + 1793 * q^4 - 1140 * q^5 - 2118 * q^6 + 1939 * q^7 - 7239 * q^8 + 33654 * q^9 - 46923 * q^10 + 5433 * q^11 + 4356 * q^12 - 4950 * q^14 + 347428 * q^15 - 400127 * q^16 - 248589 * q^17 - 19369 * q^18 + 311001 * q^19 - 927069 * q^20 + 776515 * q^21 - 1857242 * q^22 - 591609 * q^23 + 4492800 * q^24 + 3504499 * q^25 - 5801741 * q^27 - 2697168 * q^28 - 11014155 * q^29 + 6597836 * q^30 - 11574038 * q^31 + 11868417 * q^32 - 14131427 * q^33 + 10929931 * q^34 - 21112794 * q^35 - 10792871 * q^36 + 29215749 * q^37 + 7286094 * q^38 + 13661111 * q^40 - 3328377 * q^41 - 39828306 * q^42 - 6074381 * q^43 + 15912312 * q^44 - 32857342 * q^45 - 36693338 * q^46 - 22787526 * q^47 + 30270064 * q^48 - 10293266 * q^49 + 49601730 * q^50 - 68293747 * q^51 - 14740008 * q^53 - 152965386 * q^54 + 18710998 * q^55 + 7665444 * q^56 + 261681615 * q^57 + 163479359 * q^58 + 32715855 * q^59 - 94319208 * q^60 + 220502845 * q^61 + 59980476 * q^62 - 166572574 * q^63 - 462302015 * q^64 - 24064038 * q^66 - 112659045 * q^67 + 238942419 * q^68 - 86003951 * q^69 + 1020075496 * q^70 + 236450709 * q^71 - 995206683 * q^72 - 105940610 * q^73 + 455580507 * q^74 - 968954813 * q^75 + 365789708 * q^76 - 1199615445 * q^77 - 408759548 * q^79 - 580424625 * q^80 - 176914851 * q^81 - 941792217 * q^82 + 1112845728 * q^83 + 1819004068 * q^84 - 1812284636 * q^85 + 145660038 * q^86 - 69564799 * q^87 - 3178375740 * q^88 + 1154379039 * q^89 - 5112904755 * q^90 - 2272753296 * q^92 - 3136878060 * q^93 - 2755131560 * q^94 - 1779441012 * q^95 + 2953482784 * q^96 + 3616470111 * q^97 - 8263323501 * q^98 + 1131074634 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−9.18744	−0.406031	−0.203016	−	0.979175i	$-0.565074\pi$
$2$	−9.18744	−0.406031	−0.203016	+	0.979175i	$0.565074\pi$
$3$	−148.535	−1.05872	−0.529361	−	0.848397i	$-0.677568\pi$
$3$	−148.535	−1.05872	−0.529361	+	0.848397i	$0.677568\pi$
$4$	−427.591	−0.835138
$5$	1229.19	0.879536	0.439768	−	0.898111i	$-0.355061\pi$
$5$	1229.19	0.879536	0.439768	+	0.898111i	$0.355061\pi$
$6$	1364.65	0.429874
$7$	8333.07	1.31179	0.655894	−	0.754853i	$-0.272292\pi$
$7$	8333.07	1.31179	0.655894	+	0.754853i	$0.272292\pi$
$8$	8632.44	0.745124
$9$	2379.53	0.120892
$10$	−11293.1	−0.357119
$11$	−75178.8	−1.54821	−0.774103	−	0.633060i	$-0.781799\pi$
$11$	−75178.8	−1.54821	−0.774103	+	0.633060i	$0.781799\pi$
$12$	63512.0	0.884180
$13$	0	0
$13$	0	0
$14$	−76559.6	−0.532627
$15$	−182577.	−0.931184
$16$	139616.	0.532595
$17$	−212677.	−0.617591	−0.308795	−	0.951129i	$-0.599926\pi$
$17$	−212677.	−0.617591	−0.308795	+	0.951129i	$0.599926\pi$
$18$	−21861.8	−0.0490861
$19$	−447815.	−0.788328	−0.394164	−	0.919040i	$-0.628966\pi$
$19$	−447815.	−0.788328	−0.394164	+	0.919040i	$0.628966\pi$
$20$	−525590.	−0.734534
$21$	−1.23775e6	−1.38882
$22$	690701.	0.628620
$23$	1.83926e6	1.37046	0.685231	−	0.728326i	$-0.259701\pi$
$23$	1.83926e6	1.37046	0.685231	+	0.728326i	$0.259701\pi$
$24$	−1.28222e6	−0.788879
$25$	−442219.	−0.226416
$26$	0	0
$27$	2.57016e6	0.930731
$28$	−3.56314e6	−1.09552
$29$	−1.21449e6	−0.318862	−0.159431	−	0.987209i	$-0.550966\pi$
$29$	−1.21449e6	−0.318862	−0.159431	+	0.987209i	$0.550966\pi$
$30$	1.67742e6	0.378090
$31$	3.80320e6	0.739641	0.369821	−	0.929103i	$-0.379419\pi$
$31$	3.80320e6	0.739641	0.369821	+	0.929103i	$0.379419\pi$
$32$	−5.70253e6	−0.961374
$33$	1.11667e7	1.63912
$34$	1.95396e6	0.250761
$35$	1.02429e7	1.15376
$36$	−1.01746e6	−0.100962
$37$	1.69936e7	1.49066	0.745331	−	0.666695i	$-0.232292\pi$
$37$	1.69936e7	1.49066	0.745331	+	0.666695i	$0.232292\pi$
$38$	4.11427e6	0.320086
$39$	0	0
$40$	1.06109e7	0.655363
$41$	7.70454e6	0.425813	0.212907	−	0.977073i	$-0.431707\pi$
$41$	7.70454e6	0.425813	0.212907	+	0.977073i	$0.431707\pi$
$42$	1.13717e7	0.563904
$43$	2.61552e7	1.16668	0.583338	−	0.812230i	$-0.301746\pi$
$43$	2.61552e7	1.16668	0.583338	+	0.812230i	$0.301746\pi$
$44$	3.21458e7	1.29297
$45$	2.92489e6	0.106329
$46$	−1.68981e7	−0.556451
$47$	−3.99265e7	−1.19350	−0.596748	−	0.802429i	$-0.703541\pi$
$47$	−3.99265e7	−1.19350	−0.596748	+	0.802429i	$0.703541\pi$
$48$	−2.07379e7	−0.563870
$49$	2.90864e7	0.720788
$50$	4.06287e6	0.0919322
$51$	3.15899e7	0.653857
$52$	0	0
$53$	−2.84536e7	−0.495331	−0.247665	−	0.968846i	$-0.579663\pi$
$53$	−2.84536e7	−0.495331	−0.247665	+	0.968846i	$0.579663\pi$
$54$	−2.36132e7	−0.377906
$55$	−9.24090e7	−1.36170
$56$	7.19347e7	0.977445
$57$	6.65159e7	0.834620
$58$	1.11581e7	0.129468
$59$	−6.33715e7	−0.680863	−0.340432	−	0.940269i	$-0.610573\pi$
$59$	−6.33715e7	−0.680863	−0.340432	+	0.940269i	$0.610573\pi$
$60$	7.80683e7	0.777668
$61$	−1.20078e7	−0.111040	−0.0555201	−	0.998458i	$-0.517682\pi$
$61$	−1.20078e7	−0.111040	−0.0555201	+	0.998458i	$0.517682\pi$
$62$	−3.49417e7	−0.300318
$63$	1.98287e7	0.158585
$64$	−1.90920e7	−0.142246
$65$	0	0
$66$	−1.02593e8	−0.665534
$67$	−7.09554e7	−0.430179	−0.215089	−	0.976594i	$-0.569004\pi$
$67$	−7.09554e7	−0.430179	−0.215089	+	0.976594i	$0.569004\pi$
$68$	9.09388e7	0.515774
$69$	−2.73193e8	−1.45094
$70$	−9.41062e7	−0.468465
$71$	1.65210e8	0.771568	0.385784	−	0.922589i	$-0.373931\pi$
$71$	1.65210e8	0.771568	0.385784	+	0.922589i	$0.373931\pi$
$72$	2.05411e7	0.0900799
$73$	1.28511e8	0.529647	0.264823	−	0.964297i	$-0.414686\pi$
$73$	1.28511e8	0.529647	0.264823	+	0.964297i	$0.414686\pi$
$74$	−1.56128e8	−0.605255
$75$	6.56849e7	0.239712
$76$	1.91481e8	0.658363
$77$	−6.26470e8	−2.03092
$78$	0	0
$79$	6.32753e8	1.82773	0.913865	−	0.406018i	$-0.133083\pi$
$79$	6.32753e8	1.82773	0.913865	+	0.406018i	$0.133083\pi$
$80$	1.71615e8	0.468436
$81$	−4.28595e8	−1.10628
$82$	−7.07850e7	−0.172894
$83$	−1.34044e8	−0.310025	−0.155013	−	0.987912i	$-0.549542\pi$
$83$	−1.34044e8	−0.310025	−0.155013	+	0.987912i	$0.549542\pi$
$84$	5.29250e8	1.15986
$85$	−2.61420e8	−0.543193
$86$	−2.40299e8	−0.473707
$87$	1.80394e8	0.337586
$88$	−6.48977e8	−1.15360
$89$	−8.05644e8	−1.36109	−0.680547	−	0.732705i	$-0.738258\pi$
$89$	−8.05644e8	−1.36109	−0.680547	+	0.732705i	$0.738258\pi$
$90$	−2.68722e7	−0.0431730
$91$	0	0
$92$	−7.86450e8	−1.14453
$93$	−5.64906e8	−0.783075
$94$	3.66822e8	0.484597
$95$	−5.50449e8	−0.693363
$96$	8.47023e8	1.01783
$97$	7.74868e7	0.0888699	0.0444349	−	0.999012i	$-0.485851\pi$
$97$	7.74868e7	0.0888699	0.0444349	+	0.999012i	$0.485851\pi$
$98$	−2.67230e8	−0.292663
$99$	−1.78890e8	−0.187166
$100$	1.89089e8	0.189089
$101$	−2.09131e8	−0.199973	−0.0999867	−	0.994989i	$-0.531880\pi$
$101$	−2.09131e8	−0.199973	−0.0999867	+	0.994989i	$0.531880\pi$
$102$	−2.90231e8	−0.265486
$103$	−1.84658e9	−1.61659	−0.808297	−	0.588775i	$-0.799610\pi$
$103$	−1.84658e9	−1.61659	−0.808297	+	0.588775i	$0.799610\pi$
$104$	0	0
$105$	−1.52143e9	−1.22152
$106$	2.61416e8	0.201120
$107$	1.62081e9	1.19538	0.597689	−	0.801728i	$-0.296086\pi$
$107$	1.62081e9	1.19538	0.597689	+	0.801728i	$0.296086\pi$
$108$	−1.09898e9	−0.777289
$109$	2.30586e9	1.56464	0.782319	−	0.622878i	$-0.214037\pi$
$109$	2.30586e9	1.56464	0.782319	+	0.622878i	$0.214037\pi$
$110$	8.49002e8	0.552894
$111$	−2.52414e9	−1.57820
$112$	1.16343e9	0.698651
$113$	1.92207e9	1.10896	0.554479	−	0.832197i	$-0.312917\pi$
$113$	1.92207e9	1.10896	0.554479	+	0.832197i	$0.312917\pi$
$114$	−6.11112e8	−0.338882
$115$	2.26079e9	1.20537
$116$	5.19305e8	0.266294
$117$	0	0
$118$	5.82222e8	0.276452
$119$	−1.77225e9	−0.810148
$120$	−1.57609e9	−0.693848
$121$	3.29391e9	1.39694
$122$	1.10321e8	0.0450858
$123$	−1.14439e9	−0.450818
$124$	−1.62621e9	−0.617703
$125$	−2.94433e9	−1.07868
$126$	−1.82176e8	−0.0643906
$127$	−4.90251e9	−1.67225	−0.836126	−	0.548537i	$-0.815185\pi$
$127$	−4.90251e9	−1.67225	−0.836126	+	0.548537i	$0.815185\pi$
$128$	3.09510e9	1.01913
$129$	−3.88495e9	−1.23518
$130$	0	0
$131$	−8.92924e8	−0.264907	−0.132454	−	0.991189i	$-0.542286\pi$
$131$	−8.92924e8	−0.264907	−0.132454	+	0.991189i	$0.542286\pi$
$132$	−4.77476e9	−1.36889
$133$	−3.73167e9	−1.03412
$134$	6.51899e8	0.174666
$135$	3.15922e9	0.818611
$136$	−1.83592e9	−0.460182
$137$	−4.73483e9	−1.14832	−0.574158	−	0.818744i	$-0.694671\pi$
$137$	−4.73483e9	−1.14832	−0.574158	+	0.818744i	$0.694671\pi$
$138$	2.50995e9	0.589127
$139$	2.62893e9	0.597327	0.298664	−	0.954358i	$-0.403459\pi$
$139$	2.62893e9	0.597327	0.298664	+	0.954358i	$0.403459\pi$
$140$	−4.37978e9	−0.963553
$141$	5.93047e9	1.26358
$142$	−1.51786e9	−0.313281
$143$	0	0
$144$	3.32221e8	0.0643867
$145$	−1.49284e9	−0.280451
$146$	−1.18068e9	−0.215053
$147$	−4.32034e9	−0.763114
$148$	−7.26633e9	−1.24491
$149$	5.44559e9	0.905121	0.452560	−	0.891734i	$-0.350511\pi$
$149$	5.44559e9	0.905121	0.452560	+	0.891734i	$0.350511\pi$
$150$	−6.03476e8	−0.0973306
$151$	−3.29037e9	−0.515049	−0.257524	−	0.966272i	$-0.582907\pi$
$151$	−3.29037e9	−0.515049	−0.257524	+	0.966272i	$0.582907\pi$
$152$	−3.86573e9	−0.587402
$153$	−5.06071e8	−0.0746620
$154$	5.75566e9	0.824616
$155$	4.67485e9	0.650541
$156$	0	0
$157$	−8.34748e9	−1.09650	−0.548248	−	0.836316i	$-0.684705\pi$
$157$	−8.34748e9	−1.09650	−0.548248	+	0.836316i	$0.684705\pi$
$158$	−5.81338e9	−0.742116
$159$	4.22634e9	0.524418
$160$	−7.00948e9	−0.845563
$161$	1.53267e10	1.79776
$162$	3.93769e9	0.449183
$163$	−9.93338e9	−1.10218	−0.551090	−	0.834446i	$-0.685788\pi$
$163$	−9.93338e9	−1.10218	−0.551090	+	0.834446i	$0.685788\pi$
$164$	−3.29439e9	−0.355613
$165$	1.37259e10	1.44166
$166$	1.23153e9	0.125880
$167$	−1.72737e10	−1.71854	−0.859272	−	0.511518i	$-0.829083\pi$
$167$	−1.72737e10	−1.71854	−0.859272	+	0.511518i	$0.829083\pi$
$168$	−1.06848e10	−1.03484
$169$	0	0
$170$	2.40179e9	0.220554
$171$	−1.06559e9	−0.0953029
$172$	−1.11837e10	−0.974335
$173$	−1.58277e8	−0.0134341	−0.00671707	−	0.999977i	$-0.502138\pi$
$173$	−1.58277e8	−0.0134341	−0.00671707	+	0.999977i	$0.502138\pi$
$174$	−1.65736e9	−0.137071
$175$	−3.68504e9	−0.297010
$176$	−1.04962e10	−0.824566
$177$	9.41286e9	0.720845
$178$	7.40180e9	0.552647
$179$	−7.89435e9	−0.574748	−0.287374	−	0.957818i	$-0.592782\pi$
$179$	−7.89435e9	−0.574748	−0.287374	+	0.957818i	$0.592782\pi$
$180$	−1.25066e9	−0.0887997
$181$	−2.63730e10	−1.82644	−0.913221	−	0.407464i	$-0.866413\pi$
$181$	−2.63730e10	−1.82644	−0.913221	+	0.407464i	$0.866413\pi$
$182$	0	0
$183$	1.78358e9	0.117561
$184$	1.58773e10	1.02116
$185$	2.08884e10	1.31109
$186$	5.19005e9	0.317953
$187$	1.59888e10	0.956157
$188$	1.70722e10	0.996734
$189$	2.14174e10	1.22092
$190$	5.05722e9	0.281527
$191$	−3.57602e10	−1.94424	−0.972119	−	0.234490i	$-0.924658\pi$
$191$	−3.57602e10	−1.94424	−0.972119	+	0.234490i	$0.924658\pi$
$192$	2.83582e9	0.150599
$193$	−1.12148e10	−0.581815	−0.290908	−	0.956751i	$-0.593957\pi$
$193$	−1.12148e10	−0.581815	−0.290908	+	0.956751i	$0.593957\pi$
$194$	−7.11905e8	−0.0360840
$195$	0	0
$196$	−1.24371e10	−0.601958
$197$	1.82279e9	0.0862259	0.0431129	−	0.999070i	$-0.486272\pi$
$197$	1.82279e9	0.0862259	0.0431129	+	0.999070i	$0.486272\pi$
$198$	1.64354e9	0.0759954
$199$	−1.08517e10	−0.490525	−0.245262	−	0.969457i	$-0.578874\pi$
$199$	−1.08517e10	−0.490525	−0.245262	+	0.969457i	$0.578874\pi$
$200$	−3.81743e9	−0.168708
$201$	1.05393e10	0.455440
$202$	1.92138e9	0.0811955
$203$	−1.01204e10	−0.418279
$204$	−1.35076e10	−0.546061
$205$	9.47033e9	0.374518
$206$	1.69654e10	0.656388
$207$	4.37656e9	0.165679
$208$	0	0
$209$	3.36662e10	1.22049
$210$	1.39780e10	0.495974
$211$	2.73436e10	0.949695	0.474847	−	0.880068i	$-0.342503\pi$
$211$	2.73436e10	0.949695	0.474847	+	0.880068i	$0.342503\pi$
$212$	1.21665e10	0.413670
$213$	−2.45394e10	−0.816876
$214$	−1.48911e10	−0.485361
$215$	3.21497e10	1.02613
$216$	2.21868e10	0.693510
$217$	3.16923e10	0.970253
$218$	−2.11850e10	−0.635293
$219$	−1.90883e10	−0.560748
$220$	3.95132e10	1.13721
$221$	0	0
$222$	2.31904e10	0.640797
$223$	−3.21823e10	−0.871454	−0.435727	−	0.900079i	$-0.643509\pi$
$223$	−3.21823e10	−0.871454	−0.435727	+	0.900079i	$0.643509\pi$
$224$	−4.75195e10	−1.26112
$225$	−1.05227e9	−0.0273720
$226$	−1.76589e10	−0.450272
$227$	4.06286e9	0.101558	0.0507791	−	0.998710i	$-0.483830\pi$
$227$	4.06286e9	0.101558	0.0507791	+	0.998710i	$0.483830\pi$
$228$	−2.84416e10	−0.697023
$229$	−2.36623e10	−0.568587	−0.284293	−	0.958737i	$-0.591759\pi$
$229$	−2.36623e10	−0.568587	−0.284293	+	0.958737i	$0.591759\pi$
$230$	−2.07709e10	−0.489419
$231$	9.30525e10	2.15018
$232$	−1.04840e10	−0.237592
$233$	5.04339e10	1.12104	0.560519	−	0.828141i	$-0.310602\pi$
$233$	5.04339e10	1.12104	0.560519	+	0.828141i	$0.310602\pi$
$234$	0	0
$235$	−4.90772e10	−1.04972
$236$	2.70971e10	0.568615
$237$	−9.39857e10	−1.93506
$238$	1.62825e10	0.328946
$239$	−2.75780e10	−0.546728	−0.273364	−	0.961911i	$-0.588136\pi$
$239$	−2.75780e10	−0.546728	−0.273364	+	0.961911i	$0.588136\pi$
$240$	−2.54908e10	−0.495944
$241$	1.89393e10	0.361649	0.180824	−	0.983515i	$-0.442123\pi$
$241$	1.89393e10	0.361649	0.180824	+	0.983515i	$0.442123\pi$
$242$	−3.02626e10	−0.567201
$243$	1.30726e10	0.240510
$244$	5.13444e9	0.0927340
$245$	3.57527e10	0.633959
$246$	1.05140e10	0.183046
$247$	0	0
$248$	3.28309e10	0.551125
$249$	1.99102e10	0.328231
$250$	2.70509e10	0.437977
$251$	−1.85985e10	−0.295764	−0.147882	−	0.989005i	$-0.547246\pi$
$251$	−1.85985e10	−0.295764	−0.147882	+	0.989005i	$0.547246\pi$
$252$	−8.47859e9	−0.132441
$253$	−1.38273e11	−2.12176
$254$	4.50415e10	0.678987
$255$	3.88300e10	0.575091
$256$	−1.86610e10	−0.271553
$257$	8.04578e10	1.15045	0.575226	−	0.817994i	$-0.304914\pi$
$257$	8.04578e10	1.15045	0.575226	+	0.817994i	$0.304914\pi$
$258$	3.56928e10	0.501524
$259$	1.41609e11	1.95543
$260$	0	0
$261$	−2.88991e9	−0.0385480
$262$	8.20369e9	0.107561
$263$	1.18139e11	1.52263	0.761313	−	0.648385i	$-0.224555\pi$
$263$	1.18139e11	1.52263	0.761313	+	0.648385i	$0.224555\pi$
$264$	9.63955e10	1.22135
$265$	−3.49748e10	−0.435661
$266$	3.42845e10	0.419885
$267$	1.19666e11	1.44102
$268$	3.03399e10	0.359259
$269$	9.25057e9	0.107717	0.0538584	−	0.998549i	$-0.482848\pi$
$269$	9.25057e9	0.107717	0.0538584	+	0.998549i	$0.482848\pi$
$270$	−2.90251e10	−0.332382
$271$	−3.14015e9	−0.0353662	−0.0176831	−	0.999844i	$-0.505629\pi$
$271$	−3.14015e9	−0.0353662	−0.0176831	+	0.999844i	$0.505629\pi$
$272$	−2.96932e10	−0.328925
$273$	0	0
$274$	4.35010e10	0.466253
$275$	3.32455e10	0.350539
$276$	1.16815e11	1.21173
$277$	6.31727e10	0.644719	0.322359	−	0.946617i	$-0.395524\pi$
$277$	6.31727e10	0.644719	0.322359	+	0.946617i	$0.395524\pi$
$278$	−2.41531e10	−0.242534
$279$	9.04981e9	0.0894171
$280$	8.84213e10	0.859698
$281$	−8.75717e10	−0.837886	−0.418943	−	0.908012i	$-0.637599\pi$
$281$	−8.75717e10	−0.837886	−0.418943	+	0.908012i	$0.637599\pi$
$282$	−5.44858e10	−0.513053
$283$	−1.99407e11	−1.84800	−0.924000	−	0.382392i	$-0.875100\pi$
$283$	−1.99407e11	−1.84800	−0.924000	+	0.382392i	$0.875100\pi$
$284$	−7.06424e10	−0.644366
$285$	8.17607e10	0.734079
$286$	0	0
$287$	6.42024e10	0.558577
$288$	−1.35693e10	−0.116223
$289$	−7.33563e10	−0.618582
$290$	1.37154e10	0.113872
$291$	−1.15095e10	−0.0940885
$292$	−5.49500e10	−0.442328
$293$	−1.01929e11	−0.807969	−0.403984	−	0.914766i	$-0.632375\pi$
$293$	−1.01929e11	−0.807969	−0.403984	+	0.914766i	$0.632375\pi$
$294$	3.96928e10	0.309848
$295$	−7.78956e10	−0.598844
$296$	1.46697e11	1.11073
$297$	−1.93222e11	−1.44096
$298$	−5.00310e10	−0.367508
$299$	0	0
$300$	−2.80863e10	−0.200193
$301$	2.17953e11	1.53043
$302$	3.02301e10	0.209126
$303$	3.10632e10	0.211716
$304$	−6.25223e10	−0.419859
$305$	−1.47599e10	−0.0976639
$306$	4.64950e9	0.0303151
$307$	4.72074e10	0.303311	0.151655	−	0.988433i	$-0.451540\pi$
$307$	4.72074e10	0.303311	0.151655	+	0.988433i	$0.451540\pi$
$308$	2.67873e11	1.69610
$309$	2.74281e11	1.71152
$310$	−4.29499e10	−0.264140
$311$	−1.93470e11	−1.17271	−0.586356	−	0.810053i	$-0.699438\pi$
$311$	−1.93470e11	−1.17271	−0.586356	+	0.810053i	$0.699438\pi$
$312$	0	0
$313$	−1.51502e11	−0.892216	−0.446108	−	0.894979i	$-0.647190\pi$
$313$	−1.51502e11	−0.892216	−0.446108	+	0.894979i	$0.647190\pi$
$314$	7.66920e10	0.445212
$315$	2.43733e10	0.139481
$316$	−2.70559e11	−1.52641
$317$	−1.67360e10	−0.0930862	−0.0465431	−	0.998916i	$-0.514820\pi$
$317$	−1.67360e10	−0.0930862	−0.0465431	+	0.998916i	$0.514820\pi$
$318$	−3.88293e10	−0.212930
$319$	9.13039e10	0.493664
$320$	−2.34677e10	−0.125111
$321$	−2.40747e11	−1.26557
$322$	−1.40813e11	−0.729946
$323$	9.52399e10	0.486864
$324$	1.83263e11	0.923895
$325$	0	0
$326$	9.12624e10	0.447520
$327$	−3.42500e11	−1.65652
$328$	6.65089e10	0.317284
$329$	−3.32710e11	−1.56561
$330$	−1.26106e11	−0.585361
$331$	1.36079e11	0.623113	0.311556	−	0.950228i	$-0.399150\pi$
$331$	1.36079e11	0.623113	0.311556	+	0.950228i	$0.399150\pi$
$332$	5.73162e10	0.258914
$333$	4.04368e10	0.180210
$334$	1.58701e11	0.697783
$335$	−8.72176e10	−0.378358
$336$	−1.72810e11	−0.739678
$337$	1.77982e10	0.0751694	0.0375847	−	0.999293i	$-0.488034\pi$
$337$	1.77982e10	0.0751694	0.0375847	+	0.999293i	$0.488034\pi$
$338$	0	0
$339$	−2.85493e11	−1.17408
$340$	1.11781e11	0.453642
$341$	−2.85920e11	−1.14512
$342$	9.79001e9	0.0386960
$343$	−9.38905e10	−0.366267
$344$	2.25783e11	0.869318
$345$	−3.35806e11	−1.27615
$346$	1.45416e9	0.00545468
$347$	−7.07745e10	−0.262056	−0.131028	−	0.991379i	$-0.541828\pi$
$347$	−7.07745e10	−0.262056	−0.131028	+	0.991379i	$0.541828\pi$
$348$	−7.71347e10	−0.281931
$349$	1.84471e11	0.665599	0.332799	−	0.942998i	$-0.392007\pi$
$349$	1.84471e11	0.665599	0.332799	+	0.942998i	$0.392007\pi$
$350$	3.38561e10	0.120596
$351$	0	0
$352$	4.28709e11	1.48840
$353$	−1.92466e11	−0.659732	−0.329866	−	0.944028i	$-0.607004\pi$
$353$	−1.92466e11	−0.659732	−0.329866	+	0.944028i	$0.607004\pi$
$354$	−8.64801e10	−0.292686
$355$	2.03075e11	0.678622
$356$	3.44486e11	1.13670
$357$	2.63241e11	0.857722
$358$	7.25289e10	0.233366
$359$	3.62698e10	0.115245	0.0576223	−	0.998338i	$-0.481648\pi$
$359$	3.62698e10	0.115245	0.0576223	+	0.998338i	$0.481648\pi$
$360$	2.52489e10	0.0792285
$361$	−1.22150e11	−0.378539
$362$	2.42300e11	0.741593
$363$	−4.89259e11	−1.47897
$364$	0	0
$365$	1.57964e11	0.465843
$366$	−1.63865e10	−0.0477334
$367$	−2.90557e11	−0.836054	−0.418027	−	0.908435i	$-0.637278\pi$
$367$	−2.90557e11	−0.836054	−0.418027	+	0.908435i	$0.637278\pi$
$368$	2.56791e11	0.729901
$369$	1.83331e10	0.0514776
$370$	−1.91911e11	−0.532344
$371$	−2.37105e11	−0.649769
$372$	2.41549e11	0.653976
$373$	−5.17469e11	−1.38419	−0.692093	−	0.721808i	$-0.743311\pi$
$373$	−5.17469e11	−1.38419	−0.692093	+	0.721808i	$0.743311\pi$
$374$	−1.46896e11	−0.388230
$375$	4.37335e11	1.14202
$376$	−3.44663e11	−0.889302
$377$	0	0
$378$	−1.96771e11	−0.495732
$379$	−1.42775e11	−0.355447	−0.177723	−	0.984080i	$-0.556873\pi$
$379$	−1.42775e11	−0.355447	−0.177723	+	0.984080i	$0.556873\pi$
$380$	2.35367e11	0.579054
$381$	7.28192e11	1.77045
$382$	3.28544e11	0.789422
$383$	−3.28586e11	−0.780286	−0.390143	−	0.920754i	$-0.627575\pi$
$383$	−3.28586e11	−0.780286	−0.390143	+	0.920754i	$0.627575\pi$
$384$	−4.59729e11	−1.07898
$385$	−7.70050e11	−1.78626
$386$	1.03036e11	0.236235
$387$	6.22370e10	0.141042
$388$	−3.31326e10	−0.0742187
$389$	2.42006e11	0.535861	0.267930	−	0.963438i	$-0.413660\pi$
$389$	2.42006e11	0.535861	0.267930	+	0.963438i	$0.413660\pi$
$390$	0	0
$391$	−3.91168e11	−0.846385
$392$	2.51086e11	0.537076
$393$	1.32630e11	0.280463
$394$	−1.67467e10	−0.0350104
$395$	7.77773e11	1.60755
$396$	7.64917e10	0.156310
$397$	5.22893e10	0.105647	0.0528233	−	0.998604i	$-0.483178\pi$
$397$	5.22893e10	0.105647	0.0528233	+	0.998604i	$0.483178\pi$
$398$	9.96998e10	0.199168
$399$	5.54282e11	1.09484
$400$	−6.17411e10	−0.120588
$401$	2.50729e11	0.484234	0.242117	−	0.970247i	$-0.422158\pi$
$401$	2.50729e11	0.484234	0.242117	+	0.970247i	$0.422158\pi$
$402$	−9.68295e10	−0.184923
$403$	0	0
$404$	8.94225e10	0.167006
$405$	−5.26824e11	−0.973011
$406$	9.29808e10	0.169835
$407$	−1.27756e12	−2.30785
$408$	2.72698e11	0.487204
$409$	7.44848e11	1.31617	0.658086	−	0.752943i	$-0.271366\pi$
$409$	7.44848e11	1.31617	0.658086	+	0.752943i	$0.271366\pi$
$410$	−8.70081e10	−0.152066
$411$	7.03286e11	1.21575
$412$	7.89582e11	1.35008
$413$	−5.28079e11	−0.893148
$414$	−4.02094e10	−0.0672707
$415$	−1.64766e11	−0.272679
$416$	0	0
$417$	−3.90487e11	−0.632404
$418$	−3.09306e11	−0.495559
$419$	−1.22699e11	−0.194481	−0.0972405	−	0.995261i	$-0.531002\pi$
$419$	−1.22699e11	−0.194481	−0.0972405	+	0.995261i	$0.531002\pi$
$420$	6.50548e11	1.02014
$421$	9.85222e11	1.52850	0.764249	−	0.644922i	$-0.223110\pi$
$421$	9.85222e11	1.52850	0.764249	+	0.644922i	$0.223110\pi$
$422$	−2.51217e11	−0.385606
$423$	−9.50061e10	−0.144285
$424$	−2.45624e11	−0.369083
$425$	9.40500e10	0.139833
$426$	2.25455e11	0.331677
$427$	−1.00062e11	−0.145661
$428$	−6.93044e11	−0.998307
$429$	0	0
$430$	−2.95373e11	−0.416642
$431$	−1.16537e12	−1.62673	−0.813367	−	0.581751i	$-0.802368\pi$
$431$	−1.16537e12	−1.62673	−0.813367	+	0.581751i	$0.802368\pi$
$432$	3.58837e11	0.495702
$433$	−7.90752e11	−1.08105	−0.540524	−	0.841329i	$-0.681774\pi$
$433$	−7.90752e11	−1.08105	−0.540524	+	0.841329i	$0.681774\pi$
$434$	−2.91171e11	−0.393953
$435$	2.21738e11	0.296919
$436$	−9.85966e11	−1.30669
$437$	−8.23646e11	−1.08037
$438$	1.75372e11	0.227682
$439$	2.19270e11	0.281766	0.140883	−	0.990026i	$-0.455006\pi$
$439$	2.19270e11	0.281766	0.140883	+	0.990026i	$0.455006\pi$
$440$	−7.97715e11	−1.01464
$441$	6.92118e10	0.0871378
$442$	0	0
$443$	3.60046e11	0.444162	0.222081	−	0.975028i	$-0.428715\pi$
$443$	3.60046e11	0.444162	0.222081	+	0.975028i	$0.428715\pi$
$444$	1.07930e12	1.31801
$445$	−9.90288e11	−1.19713
$446$	2.95673e11	0.353838
$447$	−8.08858e11	−0.958271
$448$	−1.59095e11	−0.186597
$449$	6.93229e11	0.804949	0.402474	−	0.915431i	$-0.368150\pi$
$449$	6.93229e11	0.804949	0.402474	+	0.915431i	$0.368150\pi$
$450$	9.66770e9	0.0111139
$451$	−5.79218e11	−0.659246
$452$	−8.21858e11	−0.926134
$453$	4.88734e11	0.545293
$454$	−3.73273e10	−0.0412358
$455$	0	0
$456$	5.74195e11	0.621896
$457$	8.67582e11	0.930439	0.465219	−	0.885195i	$-0.345975\pi$
$457$	8.67582e11	0.930439	0.465219	+	0.885195i	$0.345975\pi$
$458$	2.17396e11	0.230864
$459$	−5.46615e11	−0.574810
$460$	−9.66695e11	−1.00665
$461$	−4.21197e11	−0.434342	−0.217171	−	0.976134i	$-0.569683\pi$
$461$	−4.21197e11	−0.434342	−0.217171	+	0.976134i	$0.569683\pi$
$462$	−8.54915e11	−0.873039
$463$	3.14438e10	0.0317995	0.0158998	−	0.999874i	$-0.494939\pi$
$463$	3.14438e10	0.0317995	0.0158998	+	0.999874i	$0.494939\pi$
$464$	−1.69563e11	−0.169824
$465$	−6.94377e11	−0.688742
$466$	−4.63358e11	−0.455177
$467$	−1.59083e12	−1.54774	−0.773870	−	0.633344i	$-0.781682\pi$
$467$	−1.59083e12	−1.54774	−0.773870	+	0.633344i	$0.781682\pi$
$468$	0	0
$469$	−5.91276e11	−0.564303
$470$	4.50894e11	0.426220
$471$	1.23989e12	1.16088
$472$	−5.47051e11	−0.507328
$473$	−1.96632e12	−1.80625
$474$	8.63488e11	0.785695
$475$	1.98032e11	0.178490
$476$	7.57799e11	0.676586
$477$	−6.77060e10	−0.0598818
$478$	2.53371e11	0.221989
$479$	5.73533e11	0.497793	0.248896	−	0.968530i	$-0.419932\pi$
$479$	5.73533e11	0.497793	0.248896	+	0.968530i	$0.419932\pi$
$480$	1.04115e12	0.895216
$481$	0	0
$482$	−1.74004e11	−0.146841
$483$	−2.27654e12	−1.90332
$484$	−1.40845e12	−1.16664
$485$	9.52459e10	0.0781643
$486$	−1.20104e11	−0.0976545
$487$	−2.83199e11	−0.228145	−0.114073	−	0.993472i	$-0.536390\pi$
$487$	−2.83199e11	−0.228145	−0.114073	+	0.993472i	$0.536390\pi$
$488$	−1.03657e11	−0.0827387
$489$	1.47545e12	1.16690
$490$	−3.28476e11	−0.257407
$491$	−1.56350e12	−1.21403	−0.607016	−	0.794689i	$-0.707634\pi$
$491$	−1.56350e12	−1.21403	−0.607016	+	0.794689i	$0.707634\pi$
$492$	4.89331e11	0.376495
$493$	2.58294e11	0.196926
$494$	0	0
$495$	−2.19890e11	−0.164620
$496$	5.30989e11	0.393929
$497$	1.37671e12	1.01213
$498$	−1.82924e11	−0.133272
$499$	2.35052e12	1.69712	0.848559	−	0.529100i	$-0.177470\pi$
$499$	2.35052e12	1.69712	0.848559	+	0.529100i	$0.177470\pi$
$500$	1.25897e12	0.900845
$501$	2.56574e12	1.81946
$502$	1.70872e11	0.120089
$503$	−2.10967e12	−1.46946	−0.734732	−	0.678357i	$-0.762692\pi$
$503$	−2.10967e12	−1.46946	−0.734732	+	0.678357i	$0.762692\pi$
$504$	1.71170e11	0.118166
$505$	−2.57062e11	−0.175884
$506$	1.27038e12	0.861500
$507$	0	0
$508$	2.09627e12	1.39656
$509$	1.30397e12	0.861065	0.430533	−	0.902575i	$-0.358326\pi$
$509$	1.30397e12	0.861065	0.430533	+	0.902575i	$0.358326\pi$
$510$	−3.56748e11	−0.233505
$511$	1.07089e12	0.694784
$512$	−1.41324e12	−0.908872
$513$	−1.15096e12	−0.733721
$514$	−7.39201e11	−0.467120
$515$	−2.26980e12	−1.42185
$516$	1.66117e12	1.03155
$517$	3.00163e12	1.84778
$518$	−1.30103e12	−0.793967
$519$	2.35096e10	0.0142230
$520$	0	0
$521$	−2.93717e12	−1.74646	−0.873230	−	0.487308i	$-0.837979\pi$
$521$	−2.93717e12	−1.74646	−0.873230	+	0.487308i	$0.837979\pi$
$522$	2.65509e10	0.0156517
$523$	1.49283e11	0.0872472	0.0436236	−	0.999048i	$-0.486110\pi$
$523$	1.49283e11	0.0872472	0.0436236	+	0.999048i	$0.486110\pi$
$524$	3.81806e11	0.221234
$525$	5.47357e11	0.314451
$526$	−1.08540e12	−0.618234
$527$	−8.08853e11	−0.456796
$528$	1.55905e12	0.872986
$529$	1.58171e12	0.878168
$530$	3.21329e11	0.176892
$531$	−1.50794e11	−0.0823112
$532$	1.59563e12	0.863633
$533$	0	0
$534$	−1.09942e12	−0.585099
$535$	1.99228e12	1.05138
$536$	−6.12518e11	−0.320537
$537$	1.17258e12	0.608499
$538$	−8.49891e10	−0.0437364
$539$	−2.18668e12	−1.11593
$540$	−1.35085e12	−0.683654
$541$	−6.48443e11	−0.325450	−0.162725	−	0.986671i	$-0.552028\pi$
$541$	−6.48443e11	−0.325450	−0.162725	+	0.986671i	$0.552028\pi$
$542$	2.88499e10	0.0143598
$543$	3.91730e12	1.93369
$544$	1.21280e12	0.593736
$545$	2.83434e12	1.37616
$546$	0	0
$547$	1.75877e12	0.839972	0.419986	−	0.907531i	$-0.362035\pi$
$547$	1.75877e12	0.839972	0.419986	+	0.907531i	$0.362035\pi$
$548$	2.02457e12	0.959003
$549$	−2.85730e10	−0.0134239
$550$	−3.05442e11	−0.142330
$551$	5.43866e11	0.251368
$552$	−2.35832e12	−1.08113
$553$	5.27277e12	2.39759
$554$	−5.80396e11	−0.261776
$555$	−3.10265e12	−1.38808
$556$	−1.12411e12	−0.498851
$557$	−1.69162e12	−0.744652	−0.372326	−	0.928102i	$-0.621440\pi$
$557$	−1.69162e12	−0.744652	−0.372326	+	0.928102i	$0.621440\pi$
$558$	−8.31446e10	−0.0363061
$559$	0	0
$560$	1.43008e12	0.614489
$561$	−2.37489e12	−1.01230
$562$	8.04560e11	0.340208
$563$	4.28312e12	1.79669	0.898344	−	0.439292i	$-0.144771\pi$
$563$	4.28312e12	1.79669	0.898344	+	0.439292i	$0.144771\pi$
$564$	−2.53581e12	−1.05526
$565$	2.36258e12	0.975369
$566$	1.83204e12	0.750346
$567$	−3.57151e12	−1.45120
$568$	1.42617e12	0.574914
$569$	2.10721e12	0.842757	0.421378	−	0.906885i	$-0.361546\pi$
$569$	2.10721e12	0.842757	0.421378	+	0.906885i	$0.361546\pi$
$570$	−7.51172e11	−0.298059
$571$	1.29222e12	0.508713	0.254356	−	0.967111i	$-0.418136\pi$
$571$	1.29222e12	0.508713	0.254356	+	0.967111i	$0.418136\pi$
$572$	0	0
$573$	5.31162e12	2.05841
$574$	−5.89856e11	−0.226800
$575$	−8.13355e11	−0.310295
$576$	−4.54299e10	−0.0171965
$577$	1.67362e12	0.628589	0.314295	−	0.949326i	$-0.398232\pi$
$577$	1.67362e12	0.628589	0.314295	+	0.949326i	$0.398232\pi$
$578$	6.73957e11	0.251164
$579$	1.66579e12	0.615981
$580$	6.38324e11	0.234215
$581$	−1.11700e12	−0.406688
$582$	1.05743e11	0.0382029
$583$	2.13911e12	0.766874
$584$	1.10936e12	0.394652
$585$	0	0
$586$	9.36470e11	0.328061
$587$	−3.48906e11	−0.121293	−0.0606467	−	0.998159i	$-0.519316\pi$
$587$	−3.48906e11	−0.121293	−0.0606467	+	0.998159i	$0.519316\pi$
$588$	1.84734e12	0.637306
$589$	−1.70313e12	−0.583080
$590$	7.15661e11	0.243149
$591$	−2.70747e11	−0.0912892
$592$	2.37259e12	0.793918
$593$	3.90032e12	1.29525	0.647626	−	0.761958i	$-0.275762\pi$
$593$	3.90032e12	1.29525	0.647626	+	0.761958i	$0.275762\pi$
$594$	1.77522e12	0.585076
$595$	−2.17843e12	−0.712554
$596$	−2.32848e12	−0.755901
$597$	1.61186e12	0.519329
$598$	0	0
$599$	−8.07785e11	−0.256375	−0.128187	−	0.991750i	$-0.540916\pi$
$599$	−8.07785e11	−0.256375	−0.128187	+	0.991750i	$0.540916\pi$
$600$	5.67021e11	0.178615
$601$	1.90083e11	0.0594304	0.0297152	−	0.999558i	$-0.490540\pi$
$601$	1.90083e11	0.0594304	0.0297152	+	0.999558i	$0.490540\pi$
$602$	−2.00243e12	−0.621403
$603$	−1.68840e11	−0.0520054
$604$	1.40693e12	0.430137
$605$	4.04884e12	1.22866
$606$	−2.85391e11	−0.0859635
$607$	−7.42787e11	−0.222083	−0.111041	−	0.993816i	$-0.535419\pi$
$607$	−7.42787e11	−0.222083	−0.111041	+	0.993816i	$0.535419\pi$
$608$	2.55367e12	0.757878
$609$	1.50323e12	0.442842
$610$	1.35606e11	0.0396546
$611$	0	0
$612$	2.16391e11	0.0623531
$613$	1.84386e12	0.527419	0.263709	−	0.964602i	$-0.415054\pi$
$613$	1.84386e12	0.527419	0.263709	+	0.964602i	$0.415054\pi$
$614$	−4.33716e11	−0.123154
$615$	−1.40667e12	−0.396511
$616$	−5.40797e12	−1.51328
$617$	−5.10083e12	−1.41696	−0.708480	−	0.705731i	$-0.750619\pi$
$617$	−5.10083e12	−1.41696	−0.708480	+	0.705731i	$0.750619\pi$
$618$	−2.51994e12	−0.694933
$619$	−1.32741e12	−0.363409	−0.181705	−	0.983353i	$-0.558161\pi$
$619$	−1.32741e12	−0.363409	−0.181705	+	0.983353i	$0.558161\pi$
$620$	−1.99892e12	−0.543292
$621$	4.72719e12	1.27553
$622$	1.77749e12	0.476158
$623$	−6.71348e12	−1.78547
$624$	0	0
$625$	−2.75543e12	−0.722319
$626$	1.39192e12	0.362268
$627$	−5.00059e12	−1.29216
$628$	3.56931e12	0.915726
$629$	−3.61416e12	−0.920618
$630$	−2.23928e11	−0.0566339
$631$	−5.19030e12	−1.30335	−0.651674	−	0.758499i	$-0.725933\pi$
$631$	−5.19030e12	−1.30335	−0.651674	+	0.758499i	$0.725933\pi$
$632$	5.46220e12	1.36189
$633$	−4.06147e12	−1.00546
$634$	1.53761e11	0.0377959
$635$	−6.02611e12	−1.47081
$636$	−1.80714e12	−0.437961
$637$	0	0
$638$	−8.38850e11	−0.200443
$639$	3.93122e11	0.0932768
$640$	3.80446e12	0.896362
$641$	−5.90413e12	−1.38132	−0.690661	−	0.723179i	$-0.742680\pi$
$641$	−5.90413e12	−1.38132	−0.690661	+	0.723179i	$0.742680\pi$
$642$	2.21185e12	0.513863
$643$	5.05767e12	1.16681	0.583406	−	0.812181i	$-0.301720\pi$
$643$	5.05767e12	1.16681	0.583406	+	0.812181i	$0.301720\pi$
$644$	−6.55354e12	−1.50138
$645$	−4.77534e12	−1.08639
$646$	−8.75011e11	−0.197682
$647$	−5.00696e12	−1.12332	−0.561662	−	0.827367i	$-0.689838\pi$
$647$	−5.00696e12	−1.12332	−0.561662	+	0.827367i	$0.689838\pi$
$648$	−3.69982e12	−0.824314
$649$	4.76420e12	1.05412
$650$	0	0
$651$	−4.70740e12	−1.02723
$652$	4.24742e12	0.920473
$653$	−3.70421e11	−0.0797236	−0.0398618	−	0.999205i	$-0.512692\pi$
$653$	−3.70421e11	−0.0797236	−0.0398618	+	0.999205i	$0.512692\pi$
$654$	3.14670e12	0.672598
$655$	−1.09757e12	−0.232995
$656$	1.07568e12	0.226786
$657$	3.05794e11	0.0640303
$658$	3.05676e12	0.635688
$659$	2.63115e12	0.543451	0.271726	−	0.962375i	$-0.412406\pi$
$659$	2.63115e12	0.543451	0.271726	+	0.962375i	$0.412406\pi$
$660$	−5.86908e12	−1.20399
$661$	2.29142e12	0.466872	0.233436	−	0.972372i	$-0.425003\pi$
$661$	2.29142e12	0.466872	0.233436	+	0.972372i	$0.425003\pi$
$662$	−1.25022e12	−0.253003
$663$	0	0
$664$	−1.15713e12	−0.231007
$665$	−4.58693e12	−0.909545
$666$	−3.71511e11	−0.0731708
$667$	−2.23376e12	−0.436989
$668$	7.38607e12	1.43522
$669$	4.78018e12	0.922628
$670$	8.01307e11	0.153625
$671$	9.02735e11	0.171913
$672$	7.05830e12	1.33517
$673$	−6.32811e11	−0.118907	−0.0594534	−	0.998231i	$-0.518936\pi$
$673$	−6.32811e11	−0.118907	−0.0594534	+	0.998231i	$0.518936\pi$
$674$	−1.63520e11	−0.0305211
$675$	−1.13658e12	−0.210733
$676$	0	0
$677$	−4.59387e11	−0.0840484	−0.0420242	−	0.999117i	$-0.513381\pi$
$677$	−4.59387e11	−0.0840484	−0.0420242	+	0.999117i	$0.513381\pi$
$678$	2.62295e12	0.476713
$679$	6.45702e11	0.116578
$680$	−2.25670e12	−0.404746
$681$	−6.03475e11	−0.107522
$682$	2.62687e12	0.464953
$683$	−1.19724e12	−0.210518	−0.105259	−	0.994445i	$-0.533567\pi$
$683$	−1.19724e12	−0.210518	−0.105259	+	0.994445i	$0.533567\pi$
$684$	4.55635e11	0.0795911
$685$	−5.82000e12	−1.00999
$686$	8.62613e11	0.148716
$687$	3.51467e12	0.601976
$688$	3.65170e12	0.621365
$689$	0	0
$690$	3.08520e12	0.518158
$691$	−1.14390e13	−1.90870	−0.954350	−	0.298689i	$-0.903451\pi$
$691$	−1.14390e13	−1.90870	−0.954350	+	0.298689i	$0.903451\pi$
$692$	6.76777e10	0.0112194
$693$	−1.49070e12	−0.245523
$694$	6.50236e11	0.106403
$695$	3.23145e12	0.525371
$696$	1.55724e12	0.251544
$697$	−1.63858e12	−0.262978
$698$	−1.69481e12	−0.270254
$699$	−7.49118e12	−1.18687
$700$	1.57569e12	0.248045
$701$	−7.96702e12	−1.24613	−0.623067	−	0.782169i	$-0.714114\pi$
$701$	−7.96702e12	−1.24613	−0.623067	+	0.782169i	$0.714114\pi$
$702$	0	0
$703$	−7.61000e12	−1.17513
$704$	1.43531e12	0.220227
$705$	7.28966e12	1.11136
$706$	1.76827e12	0.267872
$707$	−1.74270e12	−0.262323
$708$	−4.02485e12	−0.602005
$709$	−3.32499e12	−0.494177	−0.247088	−	0.968993i	$-0.579474\pi$
$709$	−3.32499e12	−0.494177	−0.247088	+	0.968993i	$0.579474\pi$
$710$	−1.86574e12	−0.275542
$711$	1.50565e12	0.220959
$712$	−6.95467e12	−1.01418
$713$	6.99506e12	1.01365
$714$	−2.41851e12	−0.348262
$715$	0	0
$716$	3.37555e12	0.479995
$717$	4.09628e12	0.578834
$718$	−3.33227e11	−0.0467929
$719$	1.47726e12	0.206147	0.103074	−	0.994674i	$-0.467132\pi$
$719$	1.47726e12	0.206147	0.103074	+	0.994674i	$0.467132\pi$
$720$	4.08362e11	0.0566304
$721$	−1.53877e13	−2.12063
$722$	1.12224e12	0.153699
$723$	−2.81314e12	−0.382886
$724$	1.12769e13	1.52533
$725$	5.37071e11	0.0721956
$726$	4.49504e12	0.600508
$727$	−5.16476e12	−0.685717	−0.342859	−	0.939387i	$-0.611395\pi$
$727$	−5.16476e12	−0.685717	−0.342859	+	0.939387i	$0.611395\pi$
$728$	0	0
$729$	6.49430e12	0.851644
$730$	−1.45128e12	−0.189147
$731$	−5.56261e12	−0.720528
$732$	−7.62642e11	−0.0981795
$733$	2.65026e12	0.339094	0.169547	−	0.985522i	$-0.445770\pi$
$733$	2.65026e12	0.339094	0.169547	+	0.985522i	$0.445770\pi$
$734$	2.66948e12	0.339464
$735$	−5.31051e12	−0.671186
$736$	−1.04884e13	−1.31753
$737$	5.33435e12	0.666005
$738$	−1.68435e11	−0.0209015
$739$	3.46066e12	0.426834	0.213417	−	0.976961i	$-0.431541\pi$
$739$	3.46066e12	0.426834	0.213417	+	0.976961i	$0.431541\pi$
$740$	−8.93169e12	−1.09494
$741$	0	0
$742$	2.17839e12	0.263827
$743$	−7.44309e12	−0.895990	−0.447995	−	0.894036i	$-0.647862\pi$
$743$	−7.44309e12	−0.895990	−0.447995	+	0.894036i	$0.647862\pi$
$744$	−4.87652e12	−0.583488
$745$	6.69366e12	0.796086
$746$	4.75422e12	0.562023
$747$	−3.18962e11	−0.0374797
$748$	−6.83667e12	−0.798523
$749$	1.35063e13	1.56808
$750$	−4.01799e12	−0.463696
$751$	7.42849e12	0.852159	0.426080	−	0.904686i	$-0.359894\pi$
$751$	7.42849e12	0.852159	0.426080	+	0.904686i	$0.359894\pi$
$752$	−5.57440e12	−0.635649
$753$	2.76251e12	0.313132
$754$	0	0
$755$	−4.04448e12	−0.453004
$756$	−9.15786e12	−1.01964
$757$	−7.98178e12	−0.883422	−0.441711	−	0.897157i	$-0.645628\pi$
$757$	−7.98178e12	−0.883422	−0.441711	+	0.897157i	$0.645628\pi$
$758$	1.31173e12	0.144323
$759$	2.05384e13	2.24635
$760$	−4.75171e12	−0.516641
$761$	−1.14181e12	−0.123414	−0.0617070	−	0.998094i	$-0.519654\pi$
$761$	−1.14181e12	−0.123414	−0.0617070	+	0.998094i	$0.519654\pi$
$762$	−6.69023e12	−0.718859
$763$	1.92149e13	2.05247
$764$	1.52907e13	1.62371
$765$	−6.22057e11	−0.0656680
$766$	3.01886e12	0.316821
$767$	0	0
$768$	2.77180e12	0.287499
$769$	−1.43398e13	−1.47868	−0.739340	−	0.673332i	$-0.764862\pi$
$769$	−1.43398e13	−1.47868	−0.739340	+	0.673332i	$0.764862\pi$
$770$	7.07479e12	0.725280
$771$	−1.19508e13	−1.21801
$772$	4.79536e12	0.485896
$773$	1.42374e13	1.43424	0.717119	−	0.696950i	$-0.245460\pi$
$773$	1.42374e13	1.43424	0.717119	+	0.696950i	$0.245460\pi$
$774$	−5.71799e11	−0.0572676
$775$	−1.68185e12	−0.167467
$776$	6.68900e11	0.0662191
$777$	−2.10339e13	−2.07026
$778$	−2.22341e12	−0.217576
$779$	−3.45020e12	−0.335680
$780$	0	0
$781$	−1.24203e13	−1.19455
$782$	3.59383e12	0.343659
$783$	−3.12144e12	−0.296775
$784$	4.06094e12	0.383888
$785$	−1.02606e13	−0.964407
$786$	−1.21853e12	−0.113877
$787$	−1.31208e13	−1.21920	−0.609598	−	0.792711i	$-0.708669\pi$
$787$	−1.31208e13	−1.21920	−0.609598	+	0.792711i	$0.708669\pi$
$788$	−7.79407e11	−0.0720105
$789$	−1.75478e13	−1.61204
$790$	−7.14574e12	−0.652718
$791$	1.60167e13	1.45472
$792$	−1.54426e12	−0.139462
$793$	0	0
$794$	−4.80405e11	−0.0428958
$795$	5.19497e12	0.461244
$796$	4.64011e12	0.409656
$797$	1.99597e12	0.175223	0.0876117	−	0.996155i	$-0.472077\pi$
$797$	1.99597e12	0.175223	0.0876117	+	0.996155i	$0.472077\pi$
$798$	−5.09243e12	−0.444541
$799$	8.49145e12	0.737092
$800$	2.52177e12	0.217671
$801$	−1.91705e12	−0.164546
$802$	−2.30356e12	−0.196614
$803$	−9.66128e12	−0.820001
$804$	−4.50652e12	−0.380355
$805$	1.88394e13	1.58119
$806$	0	0
$807$	−1.37403e12	−0.114042
$808$	−1.80531e12	−0.149005
$809$	1.47118e13	1.20753	0.603763	−	0.797164i	$-0.293667\pi$
$809$	1.47118e13	1.20753	0.603763	+	0.797164i	$0.293667\pi$
$810$	4.84016e12	0.395073
$811$	1.06958e13	0.868199	0.434100	−	0.900865i	$-0.357067\pi$
$811$	1.06958e13	0.868199	0.434100	+	0.900865i	$0.357067\pi$
$812$	4.32740e12	0.349321
$813$	4.66420e11	0.0374429
$814$	1.17375e13	0.937059
$815$	−1.22100e13	−0.969408
$816$	4.41047e12	0.348241
$817$	−1.17127e13	−0.919723
$818$	−6.84325e12	−0.534407
$819$	0	0
$820$	−4.04943e12	−0.312774
$821$	1.63358e13	1.25487	0.627433	−	0.778671i	$-0.284106\pi$
$821$	1.63358e13	1.25487	0.627433	+	0.778671i	$0.284106\pi$
$822$	−6.46140e12	−0.493632
$823$	−1.10509e13	−0.839648	−0.419824	−	0.907606i	$-0.637908\pi$
$823$	−1.10509e13	−0.839648	−0.419824	+	0.907606i	$0.637908\pi$
$824$	−1.59405e13	−1.20456
$825$	−4.93811e12	−0.371123
$826$	4.85170e12	0.362646
$827$	1.02665e13	0.763215	0.381608	−	0.924324i	$-0.375371\pi$
$827$	1.02665e13	0.763215	0.381608	+	0.924324i	$0.375371\pi$
$828$	−1.87138e12	−0.138365
$829$	2.47482e13	1.81990	0.909952	−	0.414713i	$-0.136118\pi$
$829$	2.47482e13	1.81990	0.909952	+	0.414713i	$0.136118\pi$
$830$	1.51378e12	0.110716
$831$	−9.38333e12	−0.682578
$832$	0	0
$833$	−6.18601e12	−0.445152
$834$	3.58758e12	0.256776
$835$	−2.12326e13	−1.51152
$836$	−1.43953e13	−1.01928
$837$	9.77484e12	0.688407
$838$	1.12729e12	0.0789654
$839$	−3.99121e12	−0.278084	−0.139042	−	0.990287i	$-0.544402\pi$
$839$	−3.99121e12	−0.278084	−0.139042	+	0.990287i	$0.544402\pi$
$840$	−1.31336e13	−0.910181
$841$	−1.30322e13	−0.898327
$842$	−9.05167e12	−0.620618
$843$	1.30074e13	0.887089
$844$	−1.16919e13	−0.793127
$845$	0	0
$846$	8.72864e11	0.0585841
$847$	2.74484e13	1.83249
$848$	−3.97259e12	−0.263811
$849$	2.96189e13	1.95652
$850$	−8.64079e11	−0.0567764
$851$	3.12557e13	2.04290
$852$	1.04928e13	0.682205
$853$	−3.00925e11	−0.0194620	−0.00973099	−	0.999953i	$-0.503098\pi$
$853$	−3.00925e11	−0.0194620	−0.00973099	+	0.999953i	$0.503098\pi$
$854$	9.19315e11	0.0591431
$855$	−1.30981e12	−0.0838223
$856$	1.39916e13	0.890705
$857$	−7.65732e12	−0.484912	−0.242456	−	0.970162i	$-0.577953\pi$
$857$	−7.65732e12	−0.484912	−0.242456	+	0.970162i	$0.577953\pi$
$858$	0	0
$859$	1.94999e13	1.22198	0.610988	−	0.791640i	$-0.290773\pi$
$859$	1.94999e13	1.22198	0.610988	+	0.791640i	$0.290773\pi$
$860$	−1.37469e13	−0.856963
$861$	−9.53628e12	−0.591377
$862$	1.07068e13	0.660505
$863$	−1.52132e13	−0.933626	−0.466813	−	0.884356i	$-0.654598\pi$
$863$	−1.52132e13	−0.933626	−0.466813	+	0.884356i	$0.654598\pi$
$864$	−1.46564e13	−0.894780
$865$	−1.94552e11	−0.0118158
$866$	7.26499e12	0.438940
$867$	1.08959e13	0.654906
$868$	−1.35513e13	−0.810295
$869$	−4.75696e13	−2.82970
$870$	−2.03721e12	−0.120559
$871$	0	0
$872$	1.99052e13	1.16585
$873$	1.84382e11	0.0107437
$874$	7.56720e12	0.438666
$875$	−2.45353e13	−1.41500
$876$	8.16197e12	0.468303
$877$	−3.08434e12	−0.176061	−0.0880307	−	0.996118i	$-0.528057\pi$
$877$	−3.08434e12	−0.176061	−0.0880307	+	0.996118i	$0.528057\pi$
$878$	−2.01453e12	−0.114406
$879$	1.51400e13	0.855415
$880$	−1.29018e13	−0.725235
$881$	1.25912e13	0.704165	0.352082	−	0.935969i	$-0.385474\pi$
$881$	1.25912e13	0.704165	0.352082	+	0.935969i	$0.385474\pi$
$882$	−6.35880e11	−0.0353807
$883$	1.13028e13	0.625696	0.312848	−	0.949803i	$-0.398717\pi$
$883$	1.13028e13	0.625696	0.312848	+	0.949803i	$0.398717\pi$
$884$	0	0
$885$	1.15702e13	0.634009
$886$	−3.30790e12	−0.180344
$887$	2.94785e13	1.59900	0.799501	−	0.600665i	$-0.205097\pi$
$887$	2.94785e13	1.59900	0.799501	+	0.600665i	$0.205097\pi$
$888$	−2.17895e13	−1.17595
$889$	−4.08529e13	−2.19364
$890$	9.09822e12	0.486073
$891$	3.22212e13	1.71274
$892$	1.37608e13	0.727785
$893$	1.78797e13	0.940866
$894$	7.43134e12	0.389088
$895$	−9.70365e12	−0.505512
$896$	2.57917e13	1.33688
$897$	0	0
$898$	−6.36900e12	−0.326834
$899$	−4.61894e12	−0.235844
$900$	4.49942e11	0.0228594
$901$	6.05142e12	0.305912
$902$	5.32153e12	0.267675
$903$	−3.23736e13	−1.62030
$904$	1.65921e13	0.826312
$905$	−3.24174e13	−1.60642
$906$	−4.49021e12	−0.221406
$907$	1.58747e13	0.778884	0.389442	−	0.921051i	$-0.372668\pi$
$907$	1.58747e13	0.778884	0.389442	+	0.921051i	$0.372668\pi$
$908$	−1.73724e12	−0.0848152
$909$	−4.97633e11	−0.0241753
$910$	0	0
$911$	−9.45057e12	−0.454596	−0.227298	−	0.973825i	$-0.572989\pi$
$911$	−9.45057e12	−0.454596	−0.227298	+	0.973825i	$0.572989\pi$
$912$	9.28672e12	0.444514
$913$	1.00773e13	0.479983
$914$	−7.97086e12	−0.377787
$915$	2.19236e12	0.103399
$916$	1.01178e13	0.474849
$917$	−7.44080e12	−0.347502
$918$	5.02200e12	0.233391
$919$	1.51181e13	0.699160	0.349580	−	0.936907i	$-0.386324\pi$
$919$	1.51181e13	0.699160	0.349580	+	0.936907i	$0.386324\pi$
$920$	1.95162e13	0.898151
$921$	−7.01194e12	−0.321122
$922$	3.86973e12	0.176356
$923$	0	0
$924$	−3.97884e13	−1.79570
$925$	−7.51492e12	−0.337510
$926$	−2.88888e11	−0.0129116
$927$	−4.39399e12	−0.195434
$928$	6.92566e12	0.306546
$929$	−3.32560e13	−1.46487	−0.732435	−	0.680837i	$-0.761616\pi$
$929$	−3.32560e13	−1.46487	−0.732435	+	0.680837i	$0.761616\pi$
$930$	6.37955e12	0.279651
$931$	−1.30253e13	−0.568217
$932$	−2.15651e13	−0.936223
$933$	2.87370e13	1.24158
$934$	1.46157e13	0.628431
$935$	1.96533e13	0.840974
$936$	0	0
$937$	3.60385e13	1.52735	0.763674	−	0.645602i	$-0.223393\pi$
$937$	3.60385e13	1.52735	0.763674	+	0.645602i	$0.223393\pi$
$938$	5.43232e12	0.229125
$939$	2.25033e13	0.944609
$940$	2.09850e13	0.876664
$941$	−1.35496e13	−0.563341	−0.281671	−	0.959511i	$-0.590889\pi$
$941$	−1.35496e13	−0.563341	−0.281671	+	0.959511i	$0.590889\pi$
$942$	−1.13914e13	−0.471355
$943$	1.41706e13	0.583561
$944$	−8.84771e12	−0.362624
$945$	2.63260e13	1.07384
$946$	1.80654e13	0.733395
$947$	−3.38186e13	−1.36641	−0.683205	−	0.730226i	$-0.739415\pi$
$947$	−3.38186e13	−1.36641	−0.683205	+	0.730226i	$0.739415\pi$
$948$	4.01874e13	1.61604
$949$	0	0
$950$	−1.81941e12	−0.0724727
$951$	2.48588e12	0.0985524
$952$	−1.52989e13	−0.603661
$953$	1.84267e13	0.723652	0.361826	−	0.932246i	$-0.382153\pi$
$953$	1.84267e13	0.723652	0.361826	+	0.932246i	$0.382153\pi$
$954$	6.22045e11	0.0243139
$955$	−4.39560e13	−1.71003
$956$	1.17921e13	0.456594
$957$	−1.35618e13	−0.522653
$958$	−5.26930e12	−0.202120
$959$	−3.94556e13	−1.50635
$960$	3.48576e12	0.132458
$961$	−1.19753e13	−0.452930
$962$	0	0
$963$	3.85676e12	0.144512
$964$	−8.09827e12	−0.302027
$965$	−1.37852e13	−0.511728
$966$	2.09156e13	0.772810
$967$	1.53512e13	0.564577	0.282288	−	0.959330i	$-0.408906\pi$
$967$	1.53512e13	0.564577	0.282288	+	0.959330i	$0.408906\pi$
$968$	2.84345e13	1.04089
$969$	−1.41464e13	−0.515454
$970$	−8.75066e11	−0.0317372
$971$	−3.33716e13	−1.20473	−0.602366	−	0.798220i	$-0.705775\pi$
$971$	−3.33716e13	−1.20473	−0.602366	+	0.798220i	$0.705775\pi$
$972$	−5.58971e12	−0.200859
$973$	2.19070e13	0.783567
$974$	2.60188e12	0.0926342
$975$	0	0
$976$	−1.67649e12	−0.0591394
$977$	3.82689e13	1.34375	0.671877	−	0.740663i	$-0.265488\pi$
$977$	3.82689e13	1.34375	0.671877	+	0.740663i	$0.265488\pi$
$978$	−1.35556e13	−0.473799
$979$	6.05673e13	2.10725
$980$	−1.52875e13	−0.529443
$981$	5.48686e12	0.189153
$982$	1.43645e13	0.492935
$983$	1.14311e13	0.390478	0.195239	−	0.980756i	$-0.437452\pi$
$983$	1.14311e13	0.390478	0.195239	+	0.980756i	$0.437452\pi$
$984$	−9.87888e12	−0.335915
$985$	2.24055e12	0.0758388
$986$	−2.37306e12	−0.0799583
$987$	4.94190e13	1.65755
$988$	0	0
$989$	4.81061e13	1.59888
$990$	2.02022e12	0.0668407
$991$	−1.23861e13	−0.407946	−0.203973	−	0.978977i	$-0.565385\pi$
$991$	−1.23861e13	−0.407946	−0.203973	+	0.978977i	$0.565385\pi$
$992$	−2.16878e13	−0.711072
$993$	−2.02125e13	−0.659703
$994$	−1.26484e13	−0.410958
$995$	−1.33388e13	−0.431434
$996$	−8.51343e12	−0.274118
$997$	3.47283e13	1.11315	0.556577	−	0.830796i	$-0.312115\pi$
$997$	3.47283e13	1.11315	0.556577	+	0.830796i	$0.312115\pi$
$998$	−2.15953e13	−0.689084
$999$	4.36765e13	1.38740

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.10.a.c.1.4		9
13.3	even	3		13.10.c.a.9.6	yes	18
13.9	even	3		13.10.c.a.3.6	✓	18
13.12	even	2		169.10.a.d.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.c.a.3.6	✓	18	13.9	even	3
13.10.c.a.9.6	yes	18	13.3	even	3
169.10.a.c.1.4		9	1.1	even	1	trivial
169.10.a.d.1.6		9	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	169.a (trivial)

\(f(q)\)	\(=\)	\(q-9.18744 q^{2} -148.535 q^{3} -427.591 q^{4} +1229.19 q^{5} +1364.65 q^{6} +8333.07 q^{7} +8632.44 q^{8} +2379.53 q^{9} -11293.1 q^{10} -75178.8 q^{11} +63512.0 q^{12} -76559.6 q^{14} -182577. q^{15} +139616. q^{16} -212677. q^{17} -21861.8 q^{18} -447815. q^{19} -525590. q^{20} -1.23775e6 q^{21} +690701. q^{22} +1.83926e6 q^{23} -1.28222e6 q^{24} -442219. q^{25} +2.57016e6 q^{27} -3.56314e6 q^{28} -1.21449e6 q^{29} +1.67742e6 q^{30} +3.80320e6 q^{31} -5.70253e6 q^{32} +1.11667e7 q^{33} +1.95396e6 q^{34} +1.02429e7 q^{35} -1.01746e6 q^{36} +1.69936e7 q^{37} +4.11427e6 q^{38} +1.06109e7 q^{40} +7.70454e6 q^{41} +1.13717e7 q^{42} +2.61552e7 q^{43} +3.21458e7 q^{44} +2.92489e6 q^{45} -1.68981e7 q^{46} -3.99265e7 q^{47} -2.07379e7 q^{48} +2.90864e7 q^{49} +4.06287e6 q^{50} +3.15899e7 q^{51} -2.84536e7 q^{53} -2.36132e7 q^{54} -9.24090e7 q^{55} +7.19347e7 q^{56} +6.65159e7 q^{57} +1.11581e7 q^{58} -6.33715e7 q^{59} +7.80683e7 q^{60} -1.20078e7 q^{61} -3.49417e7 q^{62} +1.98287e7 q^{63} -1.90920e7 q^{64} -1.02593e8 q^{66} -7.09554e7 q^{67} +9.09388e7 q^{68} -2.73193e8 q^{69} -9.41062e7 q^{70} +1.65210e8 q^{71} +2.05411e7 q^{72} +1.28511e8 q^{73} -1.56128e8 q^{74} +6.56849e7 q^{75} +1.91481e8 q^{76} -6.26470e8 q^{77} +6.32753e8 q^{79} +1.71615e8 q^{80} -4.28595e8 q^{81} -7.07850e7 q^{82} -1.34044e8 q^{83} +5.29250e8 q^{84} -2.61420e8 q^{85} -2.40299e8 q^{86} +1.80394e8 q^{87} -6.48977e8 q^{88} -8.05644e8 q^{89} -2.68722e7 q^{90} -7.86450e8 q^{92} -5.64906e8 q^{93} +3.66822e8 q^{94} -5.50449e8 q^{95} +8.47023e8 q^{96} +7.74868e7 q^{97} -2.67230e8 q^{98} -1.78890e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 15 q^{2} - 161 q^{3} + 1793 q^{4} - 1140 q^{5} - 2118 q^{6} + 1939 q^{7} - 7239 q^{8} + 33654 q^{9} - 46923 q^{10} + 5433 q^{11} + 4356 q^{12} - 4950 q^{14} + 347428 q^{15} - 400127 q^{16} - 248589 q^{17}+ \cdots + 1131074634 q^{99}+O(q^{100}) \) 9 * q - 15 * q^2 - 161 * q^3 + 1793 * q^4 - 1140 * q^5 - 2118 * q^6 + 1939 * q^7 - 7239 * q^8 + 33654 * q^9 - 46923 * q^10 + 5433 * q^11 + 4356 * q^12 - 4950 * q^14 + 347428 * q^15 - 400127 * q^16 - 248589 * q^17 - 19369 * q^18 + 311001 * q^19 - 927069 * q^20 + 776515 * q^21 - 1857242 * q^22 - 591609 * q^23 + 4492800 * q^24 + 3504499 * q^25 - 5801741 * q^27 - 2697168 * q^28 - 11014155 * q^29 + 6597836 * q^30 - 11574038 * q^31 + 11868417 * q^32 - 14131427 * q^33 + 10929931 * q^34 - 21112794 * q^35 - 10792871 * q^36 + 29215749 * q^37 + 7286094 * q^38 + 13661111 * q^40 - 3328377 * q^41 - 39828306 * q^42 - 6074381 * q^43 + 15912312 * q^44 - 32857342 * q^45 - 36693338 * q^46 - 22787526 * q^47 + 30270064 * q^48 - 10293266 * q^49 + 49601730 * q^50 - 68293747 * q^51 - 14740008 * q^53 - 152965386 * q^54 + 18710998 * q^55 + 7665444 * q^56 + 261681615 * q^57 + 163479359 * q^58 + 32715855 * q^59 - 94319208 * q^60 + 220502845 * q^61 + 59980476 * q^62 - 166572574 * q^63 - 462302015 * q^64 - 24064038 * q^66 - 112659045 * q^67 + 238942419 * q^68 - 86003951 * q^69 + 1020075496 * q^70 + 236450709 * q^71 - 995206683 * q^72 - 105940610 * q^73 + 455580507 * q^74 - 968954813 * q^75 + 365789708 * q^76 - 1199615445 * q^77 - 408759548 * q^79 - 580424625 * q^80 - 176914851 * q^81 - 941792217 * q^82 + 1112845728 * q^83 + 1819004068 * q^84 - 1812284636 * q^85 + 145660038 * q^86 - 69564799 * q^87 - 3178375740 * q^88 + 1154379039 * q^89 - 5112904755 * q^90 - 2272753296 * q^92 - 3136878060 * q^93 - 2755131560 * q^94 - 1779441012 * q^95 + 2953482784 * q^96 + 3616470111 * q^97 - 8263323501 * q^98 + 1131074634 * q^99

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